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The Hong Kong publisher whose disappearance has caused a major rift between Hong Kong and Beijing has written to a colleague to confirm that he is in China, where he is "cooperating with the authorities with an investigation".

Lee Bo, whose publishing company specialises in books critical of Beijing's Communist Party leaders, vanished last week in what legislators and experts say looks increasingly like an illegal abduction by Chinese police. He was the fifth member of the Mighty Current publishing house to vanish, amid reports that it was planning a gossipy book about the love life of Chinese President Xi Jinping.

In a fax to a colleague at Causeway Bay Books, Lee claimed to have travelled to China "by my own means, to cooperate with an investigation ... by [the] relevant department", calling his situation "good" and "normal".

But the handwritten fax, published by Taiwan's Central News Agency, raised as many questions as it answered, because Hong Kong police have said that they have no record of Lee passing through immigration, and his wife has said that he was not carrying any travel documents with him when he vanished.

In China, "assisting the authorities with an investigation" frequently equates to detention, suspicion of criminal activity and, sometimes, even torture.

With the case garnering considerable international attention, the suspicion remains that Lee was abducted by Chinese police and that he was pressured by the Chinese authorities into sending the fax. On Monday, his wife, Sophie Choi, went to Hong Kong police to withdraw her earlier complaint, according to Hong Kong's Ming Pao newspaper.

"I think it's a charade performed under duress," said Claudia Mo, a legislator with the pro-democracy Civic Party.

"He has obviously been smuggled out, but his wife has got the message that keeping a low profile would help his release, because the Chinese would save face."

Lee's disappearance was seen as an assault on Hong Kong's cherished principles of freedom of expression and autonomy from Beijing, as well as a sign that China is becoming increasingly bold in its efforts to track down and abduct dissidents and opponents outside its borders.

Hong Kong's chief executive, Leung Chun Ying, said it was "not acceptable" for Chinese police to operate independently in Hong Kong, but Leung, a Beijing loyalist, said there was "no indication" that this was what had happened.

Pro-democracy politicians said, however, that it appeared likely Lee had been kidnapped by Chinese police.

If confirmed, legislators said, Lee's abduction would be a serious violation of the "one country, two systems" principle and the Basic Law framework that has defined Beijing's relations with Hong Kong since the 1997 handover from British rule.

Lee, a major shareholder in Mighty Current and subsidiary Causeway Bay Books, disappeared from Hong Kong, before reportedly calling his wife from a number in Shenzhen, southern China, saying he was assisting in an investigation.

In October, the company's major shareholder, Gui Minhai, disappeared from his beachfront apartment in Thailand, while three employees vanished around the same time while travelling in southern China.

Democratic Party lawmaker Albert Ho said t one possible explanation for Lee's disappearance was that the Mighty Current publishing company was being pressured to scrap plans for a book rumoured to be about an old "girlfriend or mistress" of Xi.

Willy Wo-lap Lam, an adjunct professor at the Chinese University of Hong Kong, said the book was to have been titled The Lovers of Xi Jinping and would have covered the period when Xi held various official posts in Fujian province between 1985 and 2002, including after his marriage to well-known People's Liberation Army singer Peng Liyuan in 1987.